(1) Field of the Invention
The present invention relates to improvements in the art of producing optimized layouts of objects in functional organizations, including the location of building units of multiple building functional facilities and location of personnel work stations and equipments (collectively workplace elements") in functional workspaces. In one of its aspect, the invention relates to a non-metric multidimensional scaling (MDS) matrices process which optimizes these layouts according to patterns of inter-object operational criteria. In another of its aspects it relates to the measurement of crowdedness of the objects ("population density index"). In still another of its aspects it relates to a novel computational geometry technique enabling measurement of crowdedness where neither coordinate measures nor the inter-points distances but only the shape of a "convex hull" (in mathematical sense of meaning) is available.
(2) Description of the Prior Art
A paper, T. Tullis, B. B. Sperling and A. L. Steinberg (1986), "The Use of Multidimensional Scaling for Facilities Layout: An Application to the Design of the Space Station", outlines a process employing the multidimensional scaling (MDS) methodology to modify an experimental layout of a workspace of a naval vessel from at an analytical viewpoint of optimizing performance of a set of operational criteria associated with the function of the workspace on the naval vessel. However, the disclosed process make no provision for any consideration of crowdedness (population density) in connection with the modification.
An abandoned U.S. patent application Ser. No. 07/754,779 filed 30 Aug. 1991 (which is accessible to the public by virtue of it being referred to in. inter alia, a U.S. Pat. No. 5,235,506 to F. J. O'Brien, Jr.) discloses a process for calculating a form of a population density index (PDI). This abandoned application goes on to make the observation that use of PDI data in MDS would provide additional data for facilities layout. However, there is no disclosure or teaching of how to employ PDI data with MDS. Also, the form of density calculation of employed by the PDI equation disclosed therein is based upon the area of the full bounds of the quadrilateral the workspace in which a layout configuration is located. As will become apparent, of in accordance with the present invention a different form density calculation is employed in the PDI equation.
Other related references included U.S. Pat. No. 5,402,335 to F. J. O'Brien, Jr. which discloses a process for producing optimized layouts including of calculation of a non-metric PDI MDS matrix (column 24, lines 29-32, therein) which is then representing an MDS matrix of a normative ("best") a non-metric MDS matrix of other inter-object matrices (column 24, lines 35-38) are combined. As will become apparent of in accordance with the present invention, one never generates a non-metric PDI matrix and a totally different form interaction between PDI and MDS is involved. Also, the earlier mentioned U.S. Pat. No. 5,235,506, and an abandoned U.S. patent application Ser. No. 07/756,264, file Aug. 30, 1991 (but publicly available by virtue of a reference thereto, inter alia, in U.S. Pat. No. 5,235,506), each include further observations that used of PDI data in MDS would provide additional data for facilities layout. However, these observations were also made without description of a process of using PDI with MDS. As a further distinction, the PDI formula disclosed in U.S. Pat. No. 5,235,506, and that disclosed in abandoned application 07/756,264 have respective limitations of applicability to (I) a restricted number of objects and (ii) situations where an approximate density index is acceptable. Further each of the U.S. Pat. No. 5,402,335, U.S. Pat. No. 5,235,506 and abandoned application 07/756,264 disclose only forms of density calculations in their PDI formula which are based upon area of the full bounds of a quadrilateral workspace form, i.e., different from density calculation in PDI equation of the present invention.
The forms of equations supporting the calculation of PDI in all the above disclosures involving PDI have treated the density related term of the equation in ways which readily process data regarding location of the building units and workplace elements when in coordinate measurements. However, there are layout analysis problems where neither coordinate measures nor inter-point distances are available, but the layout analyst has the shape of candidate configurations from which to estimate. Illustrative examples of this problem include facility sites with impassable terrain, and/or dense forestry.
It therefore has been a continuing, but heretofore unobtained objective in the development of these layout processes for a feature enabling the process to be applied to measurements in the form of lengths of spans, as can be readily made from aerial photographs.